NAG Library Routine Document

f08bkf (dormrz)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{side}$ – Character(1)Input

On entry: indicates how $Z$ or $Z^{\mathrm{T}}$ is to be applied to $C$.

$\mathbf{side}=\text{'L'}$

$Z$ or $Z^{\mathrm{T}}$ is applied to $C$ from the left.

$\mathbf{side}=\text{'R'}$

$Z$ or $Z^{\mathrm{T}}$ is applied to $C$ from the right.

Constraint: $\mathbf{side}=\text{'L'}$ or $\text{'R'}$.

2:     $\mathbf{trans}$ – Character(1)Input

On entry: indicates whether $Z$ or $Z^{\mathrm{T}}$ is to be applied to $C$.

$\mathbf{trans}=\text{'N'}$

$Z$ is applied to $C$.

$\mathbf{trans}=\text{'T'}$

$Z^{\mathrm{T}}$ is applied to $C$.

Constraint: $\mathbf{trans}=\text{'N'}$ or $\text{'T'}$.

3:     $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of rows of the matrix $C$.

Constraint: $\mathbf{m}\ge 0$.

4:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of columns of the matrix $C$.

Constraint: $\mathbf{n}\ge 0$.

5:     $\mathbf{k}$ – IntegerInput

On entry: $k$, the number of elementary reflectors whose product defines the matrix $Z$.

Constraints:

• if $\mathbf{side}=\text{'L'}$, $\mathbf{m}\ge \mathbf{k}\ge 0$;
• if $\mathbf{side}=\text{'R'}$, $\mathbf{n}\ge \mathbf{k}\ge 0$.

6:     $\mathbf{l}$ – IntegerInput

On entry: $l$, the number of columns of the matrix $A$ containing the meaningful part of the Householder reflectors.

Constraints:

• if $\mathbf{side}=\text{'L'}$, $\mathbf{m}\ge \mathbf{l}\ge 0$;
• if $\mathbf{side}=\text{'R'}$, $\mathbf{n}\ge \mathbf{l}\ge 0$.

7:     $\mathbf{a}\left(\mathbf{lda},*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the second dimension of the array a must be at least $\max \left(1,\mathbf{m}\right)$ if $\mathbf{side}=\text{'L'}$ and at least $\max \left(1,\mathbf{n}\right)$ if $\mathbf{side}=\text{'R'}$.

On entry: the $\mathit{i}$th row of a must contain the vector which defines the elementary reflector $H_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,k$, as returned by f08bhf (dtzrzf).

8:     $\mathbf{lda}$ – IntegerInput

On entry: the first dimension of the array a as declared in the (sub)program from which f08bkf (dormrz) is called.

Constraint: $\mathbf{lda}\ge \max \left(1,\mathbf{k}\right)$.

9:     $\mathbf{tau}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array tau must be at least $\max \left(1,\mathbf{k}\right)$.

On entry: $\mathbf{tau}\left(i\right)$ must contain the scalar factor of the elementary reflector $H_i$, as returned by f08bhf (dtzrzf).

10:   $\mathbf{c}\left(\mathbf{ldc},*\right)$ – Real (Kind=nag_wp) arrayInput/Output

Note: the second dimension of the array c must be at least $\max \left(1,\mathbf{n}\right)$.

On entry: the $m$ by $n$ matrix $C$.

On exit: c is overwritten by $ZC$ or $Z^{\mathrm{T}}C$ or $CZ$ or $Z^{\mathrm{T}}C$ as specified by side and trans.

11:   $\mathbf{ldc}$ – IntegerInput

On entry: the first dimension of the array c as declared in the (sub)program from which f08bkf (dormrz) is called.

Constraint: $\mathbf{ldc}\ge \max \left(1,\mathbf{m}\right)$.

12:   $\mathbf{work}\left(\max \left(1,\mathbf{lwork}\right)\right)$ – Real (Kind=nag_wp) arrayWorkspace

On exit: if $\mathbf{info}=\mathbf{0}$, $\mathbf{work}\left(1\right)$ contains the minimum value of lwork required for optimal performance.

13:   $\mathbf{lwork}$ – IntegerInput

On entry: the dimension of the array work as declared in the (sub)program from which f08bkf (dormrz) is called.

If $\mathbf{lwork}=-1$, a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

Suggested value: for optimal performance, $\mathbf{lwork}\ge \mathbf{n}\times \mathit{nb}$ if $\mathbf{side}=\text{'L'}$ and at least $\mathbf{m}\times \mathit{nb}$ if $\mathbf{side}=\text{'R'}$, where $\mathit{nb}$ is the optimal block size.

Constraints:

• if $\mathbf{side}=\text{'L'}$, $\mathbf{lwork}\ge \max \left(1,\mathbf{n}\right)$ or $\mathbf{lwork}=-1$;
• if $\mathbf{side}=\text{'R'}$, $\mathbf{lwork}\ge \max \left(1,\mathbf{m}\right)$ or $\mathbf{lwork}=-1$.

14:   $\mathbf{info}$ – IntegerOutput

On exit: $\mathbf{info}=0$ unless the routine detects an error (see Section 6).

6

Error Indicators and Warnings

$-999<\mathbf{info}<0$

If $\mathbf{info}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.

$\mathbf{info}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

An explanatory message is output, and execution of the program is terminated.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example